Since GeometryFriends provides a Level Editor tool anyone can create levels to be played by enthusiasts and AI agents. Aside the levels that are always provided with the Competition Pack users can also download the Levels Pack (under the Downloads section) which contains levels that have been created by several developers and players of Geometry Friends.
To add the downloaded levels into the GeometryFriends game go to the Levels folder which can be found in the same location as the GeometryFriends.exe. Copy all the XML files in this pack to that folder and the game will load those levels when the game is started.